Improved Bounds for Byzantine Self-Stabilizing Clock Synchronization

The challenging task of Byzantine self-stabilizing pulse synchronization requires that, in the presence of a minority of nodes that are permanently maliciously faulty, the non-faulty nodes must start firing synchronized pulses in a regular fashion after a finite amount of time, regardless of the initial state of the system. We study this problem under full connectivity in a model where nodes have local clocks of unknown, but bounded drift, and messages are delayed for an unknown, but bounded time.

We present a generic scheme that, given a synchronous consensus protocol P, defines a self-stabilizing pulse synchronization algorithm A(P). If P terminates within R rounds (deterministically or with high probability), A(P) stabilizes within O(R) time (deterministically or with high probability, respectively). Utilizing different consensus routines, our transformation yields various improvements over previous techniques in terms of stabilization time and bit complexity. Finally, we sketch how to establish the abstraction of synchronous, integer-labeled rounds on top of pulse synchronization, at essentially the same complexity bounds. We will discuss our approach and its merits assuming no previous knowledge on the problem, however, basic familiarity with consensus will be beneficial.

Short bio: Christoph Lenzen received a diploma degree in Mathematics from the University of Bonn, Germany, and subsequently performed his graduate studies in Distributed Computing in the group of Professor Roger Wattenhofer at ETH Zurich. In 2011, he was a postdoctoral Fellow at the Hebrew University of Jerusalem, with Danny Dolev. Currently, he is a postdoctoral fellow at the Weizmann Institue of Science, with Professor David Peleg. His research interests cover distributed computing in a wider sense, including topics such as randomized load balancing, graph algorithms, and clock synchronization. He published e.g. at PODC, SPAA, FOCS, and STOC, and in JACM. In 2009, he and his coauthors received the PODC best paper award for their work on gradient clock synchronization.